Conditional Probability Worksheet

Conditional Probability Worksheet

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. In a class of 30 students, 17 are boys and 13 are girls. 5 boys and 6 girls are wearing glasses. What is the probability that a randomly selected student is a boy, given that the student is wearing glasses?

2. Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability that the second card drawn is a queen, given that the first card drawn was a king?

3. If P(A|B) = P(A), then events A and B are considered  .

4. The formula for conditional probability is P(A|B) =  .

5. A factory produces light bulbs, and 10% of the bulbs are defective. A quality control test correctly identifies 90% of defective bulbs and incorrectly identifies 5% of good bulbs as defective. If a randomly selected bulb tests positive for being defective, what is the probability that it is actually defective? Show your work.

6. If two events are mutually exclusive, then the probability of both events occurring is 0.

7. For two independent events A and B, P(A and B) = P(A) + P(B).

8. Use the Venn Diagram below to answer the following questions. The universal set U contains integers from 1 to 10. Set A represents even numbers, and Set B represents multiples of 3.

a) Find P(A|B).

b) Find P(B|A).